Thread: Arclength of linear curve

I'm to calculate the line segment y=mx+b between (x0, y0) and (x1, y1), using the formula for arclength when y is a function of x, that is:

L = (integral evaluated at a and b) (root)(1 + (f'(x))^2

Which in this case should give:

L = (integral evaluated at x0 and x1) (root) (1+m^2), as m is the derivative of mx+b.

This I get to be [(root)(1+m^2)*t]evaluated at x0 and x1, but the answer in my textbook is (1+m^2)|x0-x1|... any help would be appreciated! Thanks!

I am not sure about your books answer since m is just a constant.



this is just some arbitrary number so move outside the integral.







This what I obtained as a solution to the definite integral.

Originally Posted by gralla55

I'm to calculate the line segment y=mx+b between (x0, y0) and (x1, y1), using the formula for arclength when y is a function of x, that is:

L = (integral evaluated at a and b) (root)(1 + (f'(x))^2

Which in this case should give:

L = (integral evaluated at x0 and x1) (root) (1+m^2), as m is the derivative of mx+b.

This I get to be [(root)(1+m^2)*t]evaluated at x0 and x1, but the answer in my textbook is (1+m^2)|x0-x1|... any help would be appreciated! Thanks!

remember that you're setting up a general case arc length integral.

what if ?

Skeeter the book also got rid of the radical unless he forgot to type it.

Yes, the missing root sign is what confused me... but I guess the book could be wrong. Thanks anyway!